# The Lennard-Jones potential

## Potential form

• The Lennard-Jones (LJ) potential is one the most simplest two-body potentials used in MD simulations. The pair potential between particles $i$ and $j$ is

$$U_{ij} = 4 \epsilon_{ij} \left( \frac{ \sigma_{ij}^{12} }{ r_{ij}^{12} } - \frac{\sigma_{ij}^{6} }{ r_{ij}^{6} } \right).$$

## Parameters

 Parameter Units $\epsilon_{ij}$ eV $\sigma_{ij}$ A

## Potential file format

• If there is only one atom type, the potential file for this potential model reads
   lj 1
epsilon sigma cutoff


Here, cutoff is the cutoff distance.

• If there are two atom types, the potential file reads
   lj 2
epsilon_00 sigma_00 cutoff_00
epsilon_01 sigma_01 cutoff_01
epsilon_10 sigma_10 cutoff_10
epsilon_11 sigma_11 cutoff_11

• If there are three atom types, the potential file reads
   lj 3
epsilon_00 sigma_00 cutoff_00
epsilon_01 sigma_01 cutoff_01
epsilon_02 sigma_02 cutoff_02
epsilon_10 sigma_10 cutoff_10
epsilon_11 sigma_11 cutoff_11
epsilon_12 sigma_12 cutoff_12
epsilon_20 sigma_20 cutoff_20
epsilon_21 sigma_21 cutoff_21
epsilon_22 sigma_22 cutoff_22

• I hope the reader can understand the pattern and figure out how to prepare potential files with four and five atom types.

## Tips

• The current version of GPUMD supports up to five atom types for the LJ potential.
• The potential has not been shifted.